Chapter 5

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Unformatted text preview: Chapter
5:

Exponential
and
Logarithmic
Functions
 
 Exponential
Functions
(5.1)
 
 Definition:

Let
b
denote
a
positive
constant
other
than
1.

The
exponential
function
 with
base
b
is
defined
by
the
equation
 y = b x , b > 0, b ≠ 1
 
 Ex:
 
 
 
 
 
 
 
 Note:

 y = x 2 , y = x 

are
not
examples
of
exponential
functions.

The
base
has
to
 be
a
constant
in
order
to
qualify
as
one.
 
 
 1 Sketch:

 y = 2x 
 
 
 
 Sketch:

 y = ( )x 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Domain:
 
 
 
 
 
 
 Domain:
 
 Range:
 
 
 
 
 
 
 Range:
 
 
 Difference
between
the
two
graphs:
 Now
on
I
will
not
plot
points
to
refer
to
a
standard
exponential
function
graph.

 Instead
the
shape
as
above
will
be
drawn
for
 y = b x , b > 0, b ≠ 1
 
 Now


Sketch
:

 y = −2x 
and
compare
it
to
the
graph
of
 y = 2x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Domain:
 
 Range:
 
 Difference
between
the
two
graphs:
 
 
 
 Ex:

Sketch
 y = 2−x − 3
without
plotting
points
by
translating
and...
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This note was uploaded on 02/08/2011 for the course MATH 3 taught by Professor Staff during the Winter '08 term at University of California, Santa Cruz.

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